Utilisation de la méthode des éléments finis dans le cadre de l’inspection automatique de pièces flexibles

Par: Sasan Sattarpanah Karganroudi
Professeurs:
Jean-Christophe Cuillière
Vincent François
Souheil-Antoine Tahan
Mai. 04. 2016
Utilisation de la méthode des éléments finis dans le cadre
de l’inspection automatique de pièces flexibles
1
7ème colloque québécois sur le développement numérique de produits

layout
2
1. Introduction
• Inspection of non-rigid parts
• Fixtureless computer aided inspection
• Non-rigid registration methods
2. Sample point filtration method
• Corresponding sample points generation
• Principal curvature and von Mises stress filtration criteria
• Robustness validation of the method
3. Virtual assembly of non-rigid parts (Preliminary results)
• Estimation of necessary assembly load
4. Conclusion and future researches

Non-rigid (flexible) parts
3
Reference: ASCIONE, R. & POLINI, W. 2010. Measurement of nonrigid freeform surfaces by coordinate measuring machine. The
International Journal of Advanced Manufacturing Technology, 51, 1055-1067.
• Such as thin-walled sheet metals
• In aerospace and automotive industries
• Deform to an extent in a free-state which
exceeds the designed tolerance of model

Inspection of Non-rigid parts _ inspection fixture Vs. free-state
4
Reference: G. N. Abenhaim, S. A. Tahan, A. Desrochers, and J.-F. Lalonde, "Aerospace Panels Fixtureless Inspection Methods
with Restraining Force Requirements; A Technology Review," SAE Technical Paper 2013.
• Conventional inspection methods
• To retrieve the functional shape of
part
Elastic deformation of non-rigid parts:
• Weight
• Residual stress
• Spring back effect
• …
In a free-state Constrained in inspection fixture

Inspection fixtures Vs. Fixtureless CAI
5
Reference: ASCIONE, R. & POLINI, W. 2010. Measurement of nonrigid freeform surfaces by coordinate measuring machine. The
International Journal of Advanced Manufacturing Technology, 51, 1055-1067.
• Sophisticated
• Time consuming
• Expensive
Fixtureless computer aided inspection (CAI) methods

Fixtureless computer aided inspection
6
Measured data:
• Scan model in a free-state
• Obtain point-cloud
• In measured coordinate sys.
Designed model:
• CAD model
• In design coordinate sys.
Registration

Registration methods for a non-rigid part
7
CAD model Scanned model
Defect Elastic deformation
• Rigid registration
X
Y
X
Y
• Non-rigid registration
X
Y
Defect Elastic deformation

CAD and scan models of a typical aerospace part
9
CAD mesh Scan mesh
Bump #1
Max. amplitude: 1 mm
Area: 85 mm2
Bump #2
Max. amplitude: 1.5 mm
Area: 98 mm2
Bump #3
Max. amplitude: 1 mm
Area: 60mm2
1 m
0.5 m
Thickness: 1 mm

Generalized numerical inspection fixture (GNIF) method
10
• Based on the fact that geodesic distances are preserved during an isometric deformation
• The CAD and scan models are intrinsically the same
• Generates corresponding sample points on CAD and scan models
CAD-sp1
CAD-sp2
Scan-sp1
Scan-sp2
Correspondence
Correspondence
CAD model Scan model
Reference: RADVAR-ESFAHLAN, H. & TAHAN, S. A. 2011. Nonrigid geometric metrology using generalized numerical inspection
fixtures. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 36, 1-9

FEAnon-rigid registration on corresponding sample points
11
Corresponding sample points are evenly distributed over the CAD and scanned models
Coordinate of sample
point on CAD model
Coordinate of
corresponding sample
point on scanned model
Displacement vector
FEA non-rigid registration

Delaunay incremental point insertion
12
• Corresponding sample points are not on CAD mesh
• Insert points by Delaunay method
Sample points on CAD model CAD mesh
Inserted sample
points into CAD model

1st Finite element non-rigid registration (FENR)
13
[mm]
Displacement boundary condition
FEA
CAD model Deformed CAD model

Evaluation of defects
14
Deformed CAD model
using all sample points
Scan mesh

Scanned model
CAD model
Problem definition
15
Defects are underestimated
• Corresponding sample points close to defects may deform the CAD model to take
on the shape of defects.
The position of defects are not known a priori
in manufactured parts !!!
Objective:
• Distinguish between elastic (flexible)
deformation and deviations (defects)
Approach:
• Filtering sample points close to defects

Principal curvature differences distribution
16
Principal curvatures on defects are higher than
the general curvature value
Discrete CURV. diff. Kmax [mm-1] Discrete CURV. diff. Kmin [mm-1]
[mm-1] [mm-1]
[mm]
CAD model
Deformed CAD model
Threshold Threshold
Threshold values based on Mean distribution of principal
curvatures difference values

Filtering sample points based on curvaturecriterion, applying2nd FENR and
defect evaluation
17
Filtered sample points

von Mises stress distribution
18
[Pa] von Mises stress distribution
Deformed CAD model after
using curvature filtering
criterion
Threshold
Threshold values based on Mean distribution of von Mises stress values

Filtering more sample points based on curvature and von Mises criteria, applying
3rd FENR and defect evaluation
19

Various validation cases
20
simulation of
Scanned part
Part A
Bending
Torsion
Flexible deformation
Part B Bending
Torsion
Small (local)
Big (global)
Defects
Small (local)
Big (global)
Small (local)
Big (global)
Small (local)
Big (global)

Defect evaluation summary
21
Defect sizes are all improved based on the estimation of max.
amplitude and area.

Validation and verification (V&V) method
22
Problematic:
• Computational simulations, containing our sample point filtration method, always include
uncertainty.
Objectives:
• Assessing the level of accuracy and reliability of the method.
• Assessing the robustness by validating the method while adding noises to scan model.
Validation method:
• Based on ASME V&V 10.1 2006
• Statistic hypothesis testing (Kolmogorov-Smirnov (K-S) test)
Actual shape of
defects

Validation results by Kolmogorov-Smirnov (K-S) test
23
Kolmogorov-Smirnov (K-S) test:
• Evaluates the difference between the cumulative distribution functions (CDFs) of the
two sample data at a desired significance level.

Summary of validation results by Kolmogorov-Smirnov (K-S) test
24
BUMP1
BUMP2
BUMP3
BUMP1
BUMP2
BUMP3
• If an estimated defect shape is sufficiently similar to that of the nominal defect or not.

Conventional assembly inspection method
26
• Applying sand bags on the manufactured part with defects constrained in fixture
• Make an inspection to decide if the manufactured part can be assembled
• If deviations are more than dedicated tolerance, the part is rejected.

Assembly load estimation for non-rigid parts
27
CAD model + Assembly fixations
Scanned mesh (after rigid registration)
Constrained
mounting hole
Free
mounting hole
Mounting hole position
Permitted load
limitation
Objective Function
(Distance & Orientation mounting holes
between CAD and scan models as
function of loads)
Threshold Objective
Function Value (TOFV)
OFV < TOFV
Yes NO
Optimization method
(Fmincon in Matlab)
FF
F
F

Optimized assembly load estimation (pressures on distributed zones)
28
Fixations
Scan model
CAD model
ncad
nscn
CGSCN
CGcad
1
2
7
10
84
3
6
9
5

Optimized assembly load estimation (pressures on distributed zones)
29
Objective function (P) := (Distance + wf*Orientation)
Distance = 1000*d(CG_optim,CG_cad)
Orientation = angle between ( noptim and ncad )
Weight factor (wf) = 100
Fixations
Scan model
CAD model
ncad
nscn
1
2
7
10
84
3
6
9
5
Variables:
• Set of pressures
Limitations:
• Applying the least no. of pressures
• Pressures less than the permitted
value

Preliminary pressure optimization results
30
Objective function value = 0.33
1
2
7
10
84
3 6
9
5
Pressure
zone
1 2 3 4 5 6 7 8 9 10
Pressure
value [Pa]
21.2 0.0 0.0 0.0 0.0 0.0 0.0 19.8 31.0 0.0
Zone area
[m2]
0.024 0.031 0.035 0.049 0.069 0.061 0.046 0.030 0.040 0.062
Force value
[N]
0.509 0.000 0.000 0.000 0.000 0.000 0.000 1.235 2.338 0.000
Scan model
CAD model

Conclusion
31
• Automating the fixtureless inspection of non-rigid parts in a free-state.
• Improving the estimation of defect size in manufactured non-rigid parts.
• Validating the robustness of the improved inspection method.
• Virtually assembling a manufactured non-rigid part and reject faulty parts
before starting the assembly stage.
• Apply virtual assembly method on real cases with defects
• Study the nonlinear FE calculation effect on our simulations.
Future researches

Acknowledgement
32
• 7ème colloque québécois sur le développement numérique de produits
• National Sciences and Engineering Research Council of Canada (NSERC)
• Consortium for Aerospace Research and Innovation in Québec (CRIAQ)
• UQTR foundation

33
Thank you for your attention.

Validating case studies
Results
34

Simulation of scanned parts
35
simulation of
Scanned part
Part A
Bending
Torsion
Flexible deformation
Part B
Bending
Torsion
Small (local)
Big (global)
Defects
Small (local)
Big (global)
Small (local)
Big (global)
Small (local)
Big (global)
Bending
Torsion

Evaluation of defects (A_big defect_bending)
36
Actual: 1.5 mm
Evaluated: 0.09 mm
[mm]All generated sample points

Defect evaluation summary for partA
37

References
39
• ASCIONE, R. & POLINI, W. 2010. Measurement of nonrigid freeform surfaces by coordinate
measuring machine. The International Journal of Advanced Manufacturing Technology, 51, 1055-
1067.
• BESL, P. J. & MCKAY, N. D. 1992. A Method for Registration of 3-D Shapes. Ieee Transactions on
Pattern Analysis and Machine Intelligence, 14, 239-256.
• SABRI, V., TAHAN, S. A., PHAM, X. T., RADVAR-ESFAHLAN, H., LOUHICHI, B. & TAHVILIAN, A. M.
Fixtureless profile inspection of non-rigid parts. 43rd International Conference on Computers and
Industrial Engineering (CIE43), 2013 The university of Hong Kong. [71].1-[71].11.
• CUILLIÈRE, J.-C., FRANCOIS, V. & DROUET, J.-M. 2013. Automatic 3D mesh generation of multiple
domains for topology optimization methods. Proceedings of the 21st International Meshing
Roundtable. Springer.
• DIJKSTRA, E. W. 1959. A note on two problems in connexion with graphs. Numerische mathematik,
1, 269-271.
• MASUDA, T. & YOKOYA, N. 1995. A Robust Method for Registration and Segmentation of Multiple
Range Images. Computer Vision and Image Understanding, 61, 295-307.
• Gentilini I, Shimada K (2011) Predicting and evaluating the post-assembly shape of thin-walled
components via 3D laser digitization and FEA simulation of the assembly process. Comput Aided
Des 43(3):316–328
• Blaedel K, Swift D, Claudet A, Kasper E, Patterson S (2002) Metrology of non-rigid objects. Tech.
Rep. UCRL-ID- 146957, Lawrence Livermore National Lab

References
40
• WECKENMANN, A. & GABBIA, A. 2006. Testing formed sheet metal parts using fringe projection and
evaluation by virtual distortion compensation. Fringe 2005, 539-546.
• WECKENMANN, A., GALL, P. & GABBIA, A. 2005. 3D surface coordinate inspection of formed sheet
material parts using optical measurement systems and virtual distortion compensation. Eighth
International Symposium on Laser Metrology, 5776, 640-647.
• WECKENMANN, A., GALL, P. & HOFFMANN, J. Inspection of holes in sheet metal using optical
measuring systems. Proceedings of VIth International Science Conference Coordinate Measuring
Technique (April 21-24, 2004, Bielsko-Biala, Poland), 2004. 339-346.
• WECKENMANN, A. & WEICKMANN, J. 2006. Optical Inspection of Formed Sheet Metal Parts
Applying Fringe Projection Systems and Virtual Fixation. Metrology and Measurement Systems, 13,
321-330.
• WECKENMANN, A., WEICKMANN, J. & PETROVIC, N. Shortening of inspection processes by
virtual reverse deformation. 4th international conference and exhibition on design and production of
machines and dies/molds, Cesme, Turkey, 2007.
• ABENHAIM, G. N., DESROCHERS, A. & TAHAN, A. 2012. Nonrigid parts' specification and
inspection methods: notions, challenges, and recent advancements. International Journal of
Advanced Manufacturing Technology, 63, 741-752.
• ABENHAIM, G. N., TAHAN, A. S., DESROCHERS, A. & MARANZANA, R. 2011. A Novel Approach
for the Inspection of Flexible Parts Without the Use of Special Fixtures. Journal of Manufacturing
Science and Engineering-Transactions of the Asme, 133.
• AIDIBE, A., TAHAN, A. & ABENHAIM, G. Dimensioning control of non-rigid parts using the iterative
displacement inspection with the maximum normed residual test. International conference on
theoretical and applied mechanics. Corfu Island, Greece, 2011.
• AIDIBE, A., TAHAN, A. S. & ABENHAIM, G. N. 2012. Distinguishing profile deviations from a part's
deformation using the maximum normed residual test. WSEAS Transactions on Applied & Theoretical
Mechanics, 7.

References
41
• RADVAR-ESFAHLAN, H. 2010. Geometrical inspection of flexible parts using intrinsic geometry.
École de technologie supérieure.
• RADVAR-ESFAHLAN, H. & TAHAN, S.-A. 2013. Robust generalized numerical inspection fixture for
the metrology of compliant mechanical parts. The International Journal of Advanced Manufacturing
Technology, 1-12.
• RADVAR-ESFAHLAN, H. & TAHAN, S. A. 2011. Nonrigid geometric metrology using generalized
numerical inspection fixtures. Precision Engineering-Journal of the International Societies for
Precision Engineering and Nanotechnology, 36, 1-9.
• RIVARA, M. C. 1997. New longest‐edge algorithms for the refinement and/or improvement of
unstructured triangulations. International journal for numerical methods in Engineering, 40, 3313-
3324.
• RIVARA, M. C. & INOSTROZA, P. 1997. USING LONGEST‐SIDE BISECTION TECHNIQUES FOR
THE AUTOMATIC REFINEMENT OF DELAUNAY TRIANGULATIONS. International journal for
numerical methods in Engineering, 40, 581-597.
• SABRI, V., TAHAN, S. A., PHAM, X. T., RADVAR-ESFAHLAN, H., LOUHICHI, B. & TAHVILIAN, A. M.
Fixtureless profile inspection of non-rigid parts. 43rd International Conference on Computers and
Industrial Engineering (CIE43), 2013 The university of Hong Kong. [71].1-[71].11.
• RIVARA, M. C. 1997. New longest‐edge algorithms for the refinement and/or improvement of
unstructured triangulations. International journal for numerical methods in Engineering, 40, 3313-
3324.
• RIVARA, M. C. & INOSTROZA, P. 1997. USING LONGEST‐SIDE BISECTION TECHNIQUES FOR
THE AUTOMATIC REFINEMENT OF DELAUNAY TRIANGULATIONS. International journal for
numerical methods in Engineering, 40, 581-597.
• SETHIAN, J. A. 1996. A fast marching level set method for monotonically advancing fronts.
Proceedings of the National Academy of Sciences, 93, 1591-1595.

45
Deformed CAD model using
filtered sample points with
curvature criterion

47
GNIF method
Evaluated defects size
Corresponding Sample Points (CSP)
between CAD and scanned model
Deformed CAD using all CSP
Inspection: geometrical comparison
Sample points generating by GNIF method

48
Filtering CSP by von Mises stress criterion
GNIF method
Filtered CSP by von Mises stress criterion
Deformed CAD using filtered CSP
based on von Mises stress criterion
Sample point filtering based on von Mises stress criterion

49
Filtering CSP by Curvature criterion
GNIF method
Filtered CSP by Curvature criterion
Deformed CAD using filtered CSP
based on curvature criterion
Sample point filtering based on curvature criterion

Non-rigid (flexible) parts definition
50
Reference: G. N. Abenhaim, A. Desrochers, and A. Tahan, "Nonrigid parts' specification and inspection methods: notions, challenges,
and recent advancements," International Journal of Advanced Manufacturing Technology, vol. 63, pp. 741-752, Nov 2012.
Zones
Displacement by a reasonable force during
inspection (40 N)
Compliance behavior
A < 5 % Of the assigned tolerance Rigid
B > 10 % Of the assigned tolerance Nonrigid (Flexible)
C >> Of the assigned tolerance Extremely Nonrigid
Aerospace & automotive industries

Non-contact geometry scanner
51
Reference: Bombardier Aerospace

Computer aided inspection (CAI)
52
Measured data:
• Scanned point-cloud
• In measured coordinate sys.
Designed model:
• CAD model
• In design coordinate sys.

Non-rigid (flexible) parts definition
53
Reference: G. N. Abenhaim, A. Desrochers, and A. Tahan, "Nonrigid parts' specification and inspection methods: notions, challenges,
and recent advancements," International Journal of Advanced Manufacturing Technology, vol. 63, pp. 741-752, Nov 2012.
Aerospace & automotive industries
Rigid Non-rigid Extremely non-rigid

Registration for a non-rigid part
54
X
Y
Rigid registration
Defect
X
Y
X
Y
Y
X
Y

Delaunay incremental point insertion
55
Corresponding sample points inserted in the CAD mesh

CAD and scanned model without bump (GNIF error)
56

von Mises stress distribution without bump (GNIF error)
57
[Pa]

Curvature distribution without bump (GNIF error)
58
[mm-1] [mm-1]

Principal curvature differences distribution Gauss-Bonnet scheme
59
Discrete CURV. diff. Kmax [mm-1] Discrete CURV. diff. Kmin [mm-1][mm-1] [mm-1]
𝐾1 𝑝 = 𝐾 𝐻 𝑝 + 𝐾 𝐻
2
𝑝 − 𝐾 𝐺 𝑝
𝐾2(𝑝) = 𝐾 𝐻(𝑝) − 𝐾 𝐻
2
𝑝 − 𝐾 𝐺(𝑝)
KH : the mean curvature
KG : the Gaussian curvature

Generalized numerical inspection fixture (GNIF) method
60
• A non-rigid registration method
• Corresponding sample points
• Geodesic distances are preserved during an isometric deformation
• The CAD and scanned models are intrinsically the same
CAD-sp2 Scan-sp2
Correspondence

Corresponding sample points generated by GNIF method
61
Corresponding sample points are evenly distributed over the CAD and scanned models
FEA

Corresponding sample points generated by GNIF method
62

Defect evaluation summary (A_Big defect_Bending)
63
Actual defect size
[mm]
Evaluated defect
size [mm]
Error [%]
Using all sample points 1.5 0.09 94
Filtering sample points with the
curvature criterion only
1.5 1.59 6
curvature and von Mises criteria
successively
1.5 1.6 7

Defect evaluation summary (A_Small defects_Torsion)
64
Actual defect size
[mm]
Evaluated defect size
[mm]
Error
[%]
Average error
[%]
Using all sample points
1.0 0.14 86
801.5 0.18 88
1.0 0.35 65
1.0 0.73 27
211.5 1.22 19
1.0 0.82 18
curvature and von Mises
criteria successively
1.0 0.79 21
201.5 1.20 20
1.0 0.81 19

Defect evaluation summary (A_Big defect_Torsion)
65
Actual defect size
[mm]
Evaluated defect
size [mm]
Error [%]
Using all sample points 1.5 0.08 95
1.5 1.6 7
successively
1.5 1.68 12

Defect evaluation summary (B_Small defects_Bending)
66
Actual defect size
[mm]
[mm]
Error
[%]
Average error
[%]
1.0 0.36 64
59
2.0 0.54 73
2.0 1.11 45
1.5 0.71 53
1.0 0.78 22
16
2.0 1.82 9
2.0 1.79 11
1.5 1.18 21
1.0 0.76 24
16
2.0 1.82 9
2.0 1.75 13
1.5 1.22 19

Defect evaluation summary (B_Big defect_Bending)
67
Actual defect size
[mm]
Evaluated defect
size [mm]
Error [%]
Using all sample points 1 0.50 50
1 0.64 36
successively
1 0.83 17

Defect evaluation summary (B_Small defects_Torsion)
68
Actual defect size
[mm]
[mm]
Error
[%]
Average error
[%]
1.0 0.56 44
59
2.0 0.78 61
2.0 0.65 68
1.5 0.54 64
1.0 0.83 17
29
2.0 1.16 42
2.0 1.77 12
1.5 0.79 47
1.0 0.90 10
27
2.0 1.32 34
2.0 1.67 17
1.5 0.81 46

Defect evaluation summary (B_Big defect_Torsion)
69
Actual defect size
[mm]
Evaluated defect
size [mm]
Error [%]
Using all sample points 1 0.51 49
1 0.79 21
successively
1 0.90 10

70
Actual defect size
[mm]
[mm]
Error
[%]
Average error
[%]
1.0 0.14 86
801.5 0.18 88
1.0 0.33 67
1.0 0.72 28
211.5 1.48 1
1.0 0.66 34
1.0 0.74 26
181.5 1.47 2
1.0 0.73 27

Principal curvature differences distribution (A_big defect_bending)
71
Threshold
Threshold
Threshold
[mm-1] [mm-1]
Threshold

Filtering sample points based on curvature criterion and defect evaluation
72
Actual: 1.5 mm
Evaluated: 1.59 mm
[mm]
Comparison between:
• Deformed CAD model filtered sample points
• Scanned model

Filtering sample points based on von Mises stress criterion
73
[Pa]
von Mises stress distribution
Deformed CAD model using
filtered sample points with
curvature criterion
Threshold

Filtering more sample points based on von Mises and defect evaluation
74
Actual: 1.5 mm
Evaluated: 1.6 mm
[mm]

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